Two conservative groups joined with 15 conservative leaders on Tuesday in pushing House Republicans to take action on immigration reform.

American Principles in Action and the American Conservative Union — both of which have pressed for reforms before — said House Republicans are in a unique position to pitch their own measures.

“We, therefore, encourage the House to continue its work to address the different aspects of the immigration issue in a piecemeal basis through regular order,” the statement says.

“House Republicans should only agree to go to conference if Senate Democrats can ensure that there will be a level playing field for open debate and discussion and that they will not try to impose their own bill.”

Rather than overhauling the immigration system with a single piece of legislation, GOP lawmakers have pushed to tackle it one piece at a time.The conservative advocates say their ideal package of immigration bills should provide legal status to illegal immigrants, but not a special path to citizenship; establish border security triggers; and target foreign workers’ role in the labor market.

Last week, three House GOP members made the unexpected move of signing on to a Democratic-led immigration bill in the House, which Rep. Joe Garcia introduced in early October.

Republican Reps. Jeff Denham, David Valadao and Ileana Ros-Lehtinen are now co-sponsors of the measure.

President Obama is pressuring House Republicans to pass an immigration bill by the end of the year.

Obama and Vice President Biden are meeting with CEOs of State Farm, Marriott and McDonalds at the White House Tuesday to discuss immigration reform.